The average Bottom-hadron and individual B^+, B^0, and B^0_s meson
lifetimes have been determined using decays with a J/psi -> mu^+mu^- in the
final state.  The data sample consists of 110 pb^-1 of pbar p collisions at
sqrt s = 1.8 TeV collected by the CDF detector at the Fermilab Tevatron
collider during 1992-1995.  For the average lifetime of B-hadrons decaying
into J/psi + X, we obtain (tau_b) = 1.533 +/- 0.015(stat) ^+0.035
_-0.031(syst) ps.  For the B^+ and B^0 meson lifetimes, we determine tau(B^+)
= 1.68 +/- 0.07(stat) +/- 0.02 (syst) ps, tau(B^0) = 1.58 +/- 0.09(stat) +/-
0.02(syst) ps, and tau(B^+)/tau(B^0) = 1.06 +/- 0.07(stat) +/- 0.02 (syst).
For the B^0_s meson lifetime, we find tau(B^0_s) = 1.34^+0.23_ _0.19(stat) +/-
0.05(syst) ps.